Tag Archives: sex

No need to do politics. Just take a statistical course. And I do not talk about misinterpretation of statistics, but I talk about the mathematical foundations of statistical tests.
Consider the following parametric test, with a one-dimensional parameter: versus , for some (fixed) . A standard way of doing such a test is to consider an rejection region . The test works as follows: consider a sample ,

if , then we accept

if , the we reject

For instance, consider the case of a Bernoulli sample, with probability . The standard idea is to define

The rejection region is then based on statistic ,

if , then we accept

if , the we reject

where threshold is taken so that the probability to make a first type error is (say 5%) using the Gaussian approximation for z. Here

Thus, the acceptation region is then the green area below, while the rejection region is the red one, for .

Consider now the exact opposite test (with the same ), versus . Here, we use the same statistics, and the test is

if , then we accept

if , the we reject

where now

Thus, now, the acceptation region is then the green area below, while the rejection region is the red one.

So if we summarize what we just said,

in the region on the left below, both test agree that

in the region on the right below, both test agree that

and in the region in blue, in the middle, the two tests disagree (one claims that , and the other one that )

Here is the evolution of the region as a function of (the size of the sample) when the sample frequency is 20%. With a small sample size, we can hardly say anything.

Here, when the sample frequency is 20% and is equal to 10, we accept at the same time that theta is higher than 50% and lower than 50%.
And obviously it is not only a theoretical problem: it has obviously some strong implications. This morning, a good friend mentioned a post published some months ago, online here, about discrimination, and the lack of women with academic positions in mathematics, in France. As claimed by the author of the post“A Paris VI, meilleure université française selon son président, sur 11 postes de maitres de conférences, 5 filles classées premières. Il y a donc des filles excellentes ? A Toulouse, sur 4 postes, 2 filles premières. Parité parfaite. Mais à côté de cela, Bordeaux, 4 postes, 0 fille première. Littoral, 3 postes, 0 fille, Nice, 5 postes, 0 fille, Rennes, 7 postes, 0 fille…”.
Consider the latter one: in Rennes, out of 7 people hired last year, no woman. So in some sense, it looks obvious that there is some kind of discrimination ! Zero out of seven ! Well, if we consider the fact that around 30% of PhD thesis in mathematics were defended by women those years, we can also try to see is there if no “positive discrimination“, i.e. test where theta is the probability to hire a woman (just to be a little bit provocative).

With no woman hired that year, we can still pretend that there was some kind of “positive discrimination“. An note that we do accept – with more confidence – the assumption of “positive discrimination” if we look at all universities together,

Some
sort of unpretentious (academic) blog, by a surreptitious economist and
born-again mathematician. A blog activist, and an actuary, too. Always curious.
Because academics are probably more than the sum of our publication lists, grants and conference talks...

Used to live in Paris (France),
Leuven (Belgium), Hong-Kong (China), and Montréal (Canada). Professor and researcher in
Montréal, currently back in Rennes (France). ENSAE ParisTech & KU Leuven Alumni